As some of the examples below would suggest, Fun with Acronyms is practically a necessity.

In Real Life, the UN has no military force of its own, and acts primarily through sanctions, when its members can be made to agree on anything in the first place. UN "military" are generally peacekeeping forces made up of units and equipment volunteered from member nations. As a result, many instances of this trope require that the UN adjust its structure to become much more powerful; frequently there is some form of world-threatening crisis that demands a unified multi-national force under UN command that results in the UN becoming far stronger.

Earlier works using this trope tend to portray the UN as the good guys. They represent the best aspects of humanity, doing its best to protect freedom; many of the nations named are usually nations with known democratic governments, thus making the alliance more akin to NATO. Latter works will show the Super UN as either overly bureaucratic (at best) or as an evil empire (at worse).

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The UN in Neon Genesis Evangelion, having undergone heavy reforms following the Second Impact and the Valentine Treaty of February 2001. To illustrate, all of the world's national militaries are explicitly under direct control of the UN - and are effectively subordinate to UN Special AgencyNERV.

In Darker Than Black, The Syndicate runs the U.N., which makes it a very powerful organization probably more so than actual nations. IIRC, PANDORA is basically their own army.

In Mobile Suit Gundam 00, the UN starts off like its real world counterpart: lacking influence and mostly dealing with humanitarian efforts. Once the power blocs begin to work together, a joint military force is formed under the aspects of the UN. Eventually, the superpowers reform the UN into the Earth Sphere Federation.

The U.N. in THUNDER Agents stands for United Nations (The Higher United Nations Defense Enforcement Reserves), but I'm not sure how directly associated with the UN they are.

In the Wildstorm Universe, this is basically the case for the international super-team Stormwatch. Its team members actually get a lot of flak from America, which, in this continuity, wish they were the world police.

In Marvel Comics, SHIELD wavers back and forth between being a UN peacekeeping force and being affiliated with the USA exclusively.

The UN is militarized in The Animatrix, (and is apparently far more powerful by this time) as a direct result of humanity uniting against the Machines.

Used in the A Thief in the Night films (a Christian End Times series). After the Rapture and subsquent emergency, the UN reforms itself into the UN Imperium of Total Emergency. It proceeds to do evil: forcing people to get branded, controlling food supplies, having their own secret police, etc.

The U.N. was depicted this way in Left Behind, which is why the Anti Christ went for a job as Secretary General. Hilariously, it's treated as though the United Nations has always been this powerful. (For why, see Conspiracy Theories).

This is the Case in Daniel Keys Moran's Tales of the Continuing Time cycle. The French have begun to dominate the UN, and the peacekeeping forces are now known and feared as peaceforcers.

In Charles Stross' Eschaton series, the UN, consisting of most of the microstates of the balkanized post-Singularity Earth, is an interesting mix of "quite powerful" and "not very powerful at all": it mostly leaves local governments on Earth alone, but it has scores of agents tasked with enforcing the laws of the Eschaton--a far-future expression of the Singularity that flung human civilizations across space for reasons unclear, but which wants the laws of causality to be preserved at any cost. It also a lot of pull for the mythical association with Earth-That-Was (which they usually can't distinguish from Earth-That-Still-Is).

It should be noted that this UN is not the same organization, but rather a development of the Internet Engineering Task Force (yes) that took on the responsibilities and form of the UN after the post-Singularity Earth had settled down (i.e. suitably modified for a world of tens of thousands of states rather than 193).

Larry Niven's Known Space has the UN develop into a planetary government.

Shah Guido G, a short story by Isaac Asimov, has the UN ultimately transform into a tyrannical, caste-based oppressive regime headed by a hereditary Sekjen (Secretary General, in other words), only to fall when one of the high caste arranges for the flying capital city of Atlantis to crash after seeing just how corrupt the society has become. The reason for the name of the story is in-universe a nickname by the oppressed masses for the last Sekjen, and out-universe a reference to the Asimov-admitted point of the story being to set the stage for an Incredibly Lame Pun.

Poul Anderson's The Psychotechnic League has the UN reforming into a superpower after a nuclear conflict in 1958. However, many nationalists oppose this, and the UN sends special agents (UNMen) to defuse threats. Unlike some other examples, the UN are the good guys.

David Feintuch's Seafort Saga has the UN as the governing body of Earth and its colonies. Oddly enough, it's society is akin to Napoleonic-era Britain: Swearing in public can lead to legal trouble, The Church is an important factor of life, and there are legal duels.

The 2005 revival of Doctor Who imagines the UN having much more control, organization, and respect than it does in real life, what with controlling the launch of nuclear weapons and issuing global advisories during alien invasions and worldwide crises. Ironically, for real-life political reasons, super-spy/alien-fighting organization UNIT is no longer part of the United Nations.

Subverted by Babylon 5: The UN wasn't turning into this fast enough for the big dogs of 22nd-century Earth, so they established the stronger Earth Alliance to replace it, and crushed the holdouts. Being The Federation in its most realistic form, it continues to have UN-ish elements, like preserving national states back on Earth.

The USN in the Jovian Chronicles is an independent military peace-keeping and police force descended from the UN.

Cthulhu Tech had the New United Nations which came about when the US, EU, and Russia decided that they wanted international law to have some actual teeth and support for democratic principles. That lasted about 40 years until an alien invasion caused the NUN to turn into the New Earth Government police state to fight for survival in a Lovecraft Lite setting.

In a strange subversion Blue Planet gives us the Global Ecology Organization (GEO) which was one of the last vestiges of the UN in the face of an agriculture destroying Blight. A century after being given control of Earth's military and scientific resources, it is now being challenged by the rest of a reinstituted UN who sees it as a dangerous relic.

In Feng Shui the Buro is the Police State born from the UN's peace-keeping forces when an ambitious scientist used knowledge of arcanowave science to seize control of the flow of the world's chi and the reigns of power with it.

In Traveller the UN evolved into the Terran Confederation, which was strong enough to fight the Vilani.

The default setting for GURPS Supers featured a UN with quietly held tactical nuclear weapons. And the ability to tell nations to not make strategic ones.

The United Nations in Halo founded both the Unified Earth Government (UEG) and the UN Space Command (UNSC); the UEG absorbed its parent organization into one of its branches, but was itself eventually subsumed during the Human-Covenant War — by the UNSC, which now rules all of humanity in the Milky Way galaxy.

This happens over the course of the Command and Conquer Tiberium series. The United Nations Global Defense Initiative was founded as a black-ops, anti-terrorist unit, but is reformed into what is essentially the UN's military in response to the Brotherhood of Nod's coalition of disaffected Third World nations. But as Tiberium spreads across the planet, most of the UN's member nations collapse under the strain of dealing with the catastrophic ecological damage, leaving GDI as the only organization capable of keeping order. By Tiberium Wars the United Nations has been effectively subsumed by GDI, a would-be One World Order opposed by its old enemy the Brotherhood of Nod, which has performed a similar stabilizing role in the Tiberium-racked Third World.

Deus Ex has UNATCO, the "United Nations Anti-Terrorist Coalition", which while on the surface, seems to be a world police force hosted by the UN, is pretty much the beginnings of a military for a one-state world. The UN itself apparently has much more power in the 2050s, since it appears holds sway over politics in nations, as one character uses the term, "UN-governed nations." The UN's influence got to be so bad, that China left it sometime before the game, and is arguably better off for it. Conversations and flavor text materials in the game suggest that much of this came about because citizen confidence in local sovereign states has severely waned in the wake of ecological and economic disasters, weakening those states, which in turn causes them to increasingly rely on the UN to maintain their influence, consolidating effective power there. This in turn reduces citizen confidence in those states further, leading to widespread discontentment and open civil war in first world nations.

Mission Critical is based on the idea of UN waging a war with The Alliance (which includes US) over AI research and slowly winning thanks to superior Attack Drone technology. UN believes that AI research will lead to Armageddon and wishes to ban it worldwide, while the Alliance pretty much takes a page out of Patrick Henry's book (i.e. "Give me liberty or give me death").

The United Nations of Sol in Schlock Mercenary is the primary human military power in the galaxy and has several Battleplates the size of Manhattan that can crack planets. Also the protagonists frequently end up entangled in their top-secret research projects.

There is also "The League of Galactics", which by context is taken about as seriously as the League of Nations would be were it still around.

In the Global Guardians PBEM Universe, the UN gains actual political power through its control of alien technology (when the alien traders visited earth, they'd only negotiate with 'the planet's government' and not with any individual nation on the planet). Are you a world leader and want your nation to have access to room-temperature superconductors, compact fusion reactors, and miracle drugs that cure cancer? Better toe the UN line then...